The function f(x)=4-x^2 4 x-x^3 is - Vidyadip

MCQ

The function $f(x)=\frac{4-x^2}{4 x-x^3}$ is

A
discontinuous at only one point
B
discontinuous at exactly two points
✓
discontinuous at exactly three points
D
None of these

✓

Answer

Correct option: C.

discontinuous at exactly three points

(c) : $f(x)=\frac{4-x^2}{4 x-x^3}=\frac{4-x^2}{x(2-x)(2+x)}$
So, $f(x)$ is discontinuous at $x=0,2,-2$.

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